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<h1 class="reftitle">invariantSet</h1>
<h2>Purpose</h2>
<p>Computation of invariant sets for linear systems</p>
<h2>Syntax</h2>
<pre class="synopsis">S = system.invariantSet()</pre>
<pre class="synopsis">S = system.invariantSet('X', X, 'U', U)</pre>
<h2>Description</h2>
<p></p> 
    For an autonomous LTI system <img src="../../../../../fig/mpt/modules/ui/@LTISystem/invariantset1.png" alt="../../../../../fig/mpt/modules/ui/@LTISystem/invariantset1.png"> this function
    computes the set of states for which recursive satisfaction of
    state constraints can be shown.<br><br>

    The set is computed by running the set recursion
    <p class="programlistingindent"><img src="../../../../../fig/mpt/modules/ui/@LTISystem/invariantset9.png" alt="../../../../../fig/mpt/modules/ui/@LTISystem/invariantset9.png"></p>
    initialized by <img src="../../../../../fig/mpt/modules/ui/@LTISystem/invariantset2.png" alt="../../../../../fig/mpt/modules/ui/@LTISystem/invariantset2.png"> and terminating once
    <img src="../../../../../fig/mpt/modules/ui/@LTISystem/invariantset3.png" alt="../../../../../fig/mpt/modules/ui/@LTISystem/invariantset3.png">. If <img src="../../../../../fig/mpt/modules/ui/@LTISystem/invariantset4.png" alt="../../../../../fig/mpt/modules/ui/@LTISystem/invariantset4.png"> is not provided, <img src="../../../../../fig/mpt/modules/ui/@LTISystem/invariantset5.png" alt="../../../../../fig/mpt/modules/ui/@LTISystem/invariantset5.png"> is assumed.<br><br>
    
    For an LTI system <img src="../../../../../fig/mpt/modules/ui/@LTISystem/invariantset6.png" alt="../../../../../fig/mpt/modules/ui/@LTISystem/invariantset6.png">, which is subject to
    polyhedral state constraints <img src="../../../../../fig/mpt/modules/ui/@LTISystem/invariantset7.png" alt="../../../../../fig/mpt/modules/ui/@LTISystem/invariantset7.png"> and input constraints
    <img src="../../../../../fig/mpt/modules/ui/@LTISystem/invariantset8.png" alt="../../../../../fig/mpt/modules/ui/@LTISystem/invariantset8.png"> this function
    calculates the maximal control-invariant set
    
    <p class="programlistingindent"><img src="../../../../../fig/mpt/modules/ui/@LTISystem/invariantset10.png" alt="../../../../../fig/mpt/modules/ui/@LTISystem/invariantset10.png"></p>

    Note that this function requires that state constraints
    defined in <tt>system.x.min</tt> and <tt>system.x.max</tt> (see
    "<tt>help SystemSignal</tt>").
  <h2>Input Arguments</h2>
<table cellspacing="0" class="body" cellpadding="4" border="0" width="100%">
<colgroup>
<col width="31%">
<col width="69%">
</colgroup>
<tbody>
<tr valign="top">
<td><tt>X</tt></td>
<td>
<p></p>Polyhedron defining state constraints (optional)<p>
	    		Class: <tt>polyhedron</tt></p>
</td>
</tr>
<tr valign="top">
<td><tt>U</tt></td>
<td>
<p></p>Polyhedron defining input constraints (optional)<p>
	    		Class: <tt>polyhedron</tt></p>
</td>
</tr>
<tr valign="top">
<td><tt>maxIterations</tt></td>
<td>
<p></p>Maximal number of iterations (optional)<p>
	    		Class: <tt>double</tt></p>
</td>
</tr>
</tbody>
</table>
<h2>Output Arguments</h2>
<table cellspacing="0" class="body" cellpadding="4" border="0" width="100%">
<colgroup>
<col width="31%">
<col width="69%">
</colgroup>
<tbody><tr valign="top">
<td><tt>S</tt></td>
<td>
<p></p>Invariant set<p>
	    		Class: <tt>Polyhedron</tt></p>
</td>
</tr></tbody>
</table>
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<br><p>©  <b>2003-2013</b>     Michal Kvasnica: STU Bratislava,    <a href="mailto:michal.kvasnica@stuba.sk">michal.kvasnica@stuba.sk</a></p>
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